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+ 9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0 is prime. [Silva]

+ If the digit sum of n!, S(n!), is the product of 9 and any prime larger than n, then S(n!) cannot divide n!.

+ All digits of the prime 2 * 103020 - 1 are 9 except 1. It contains 3021 digits. [Williams]

+ The sum of the first 9 consecutive prime numbers = 102, a perfect square.

+ If odd perfect numbers exist, they are of the forms 12n + 1 ... or 36n + 9. [Touchard]

+ 9 is the smallest April Fool prime.

+ For every prime p with p not equal to 2 and p not equal to 5, there is some number with all digits equal to 9 such that p divides evenly into this number.

+ Goldbach conjectured that every odd integer greater than or equal to 9 can be represented as the sum of three odd primes.

+ There are no consecutive-digit primes starting with 9 with digits in descending order. [Madachy]

+ Define a certain number of irregularly marked points, n, along the rim of a paper circle, then cut along straight lines that join all possible pairs of points. If n = 9, a prime number of separate pieces will be created. 163 to be exact!

+ The smallest odd Giuga number must have at least 9 prime factors.

+ If a is greater than b, and b is greater than or equal to 1, then an + bn has a primitive prime factor with the exception of 23 + 13 = 9.

+ 9 times the 9th prime has a sum of digits equal to 9.

+ There are no clusters (groups) of 9 twin prime pairs less than 1014. [DeVries]

+ Washington University in St. Louis provides a page that calculates the prime factors of a number (with a maximum of 9 digits).

+ There are at least 9 prime numbers between x3 and (x + 1)3 for x greater than or equal to pi, assuming the Riemann Hypothesis is true.

+ The smallest odd composite number. [Gupta]

+ 109 + 9 is prime. [Gupta]

+ Two raised to the 9th power plus and minus 9 are primes! [Hoefakker]

+ The first digit to appear as an end-digit in two consecutive primes (139 and 149). [Silva]

+ 19, 109, 1009 and 10009 are primes. No other digit can replace the 9 and yield four primes. [Friend]

+ The number of known positive integers which are the sum of two primes in exactly two ways is a prime square. [Capelle]

+ 2^^n-9 = 2^(2^(2^(....(2^2)...)))-9 is (for large enough n) always divisible by both 7 and 11. Note that 9 is midway between 7 and 11. [Hartley]

+ The are exactly 3=(sqrt(9)) pandigital improper fractions that reduce to 9 (provided each digit is used once). [Patterson]

+ 9 is the only number m such that m = pi(pi(m)!). [Firoozbakht]

+ The 9th Fibonacci number plus 9 is prime. [Losnak]

+ The only composite digit that can appear as end-digit of a prime. [Silva]

+ The only non-prime digit that is the difference of consecutive squares. [Silva]

+ 10*(22n + 1) + 9 gives primes for n = 1 to 7. Therefore, there are 7 known Fermat numbers which yields primes when a 9 is appended. [Wesolowski]

+ The smallest composite number n such that both 2n+n and 2n-n are prime. That is, 29+9 = 521 and 29-9 = 503 are prime. [Poo Sung]

+ 9+8^7+6^5+4^3+2^1 is prime. [Silva]

+ Three more semiprimes can be consecutively formed from 9 by iterating the process described in A227942.

+ The only known integer n, such that 2^n-n^2 and 2^n+n^2 are both primes, i.e., 431 and 593. [Loungrides]

(There are 8 curios for this number that have not yet been approved by an editor.)




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